"集合"由来演化的哲学思考

"集合"已成为现代数学的核心概念,它是人类认识事物、现象等的一种模式.迄今科学家们提出了三种重要的集合概念Cantor集合、Fuzzy集合、Extension集合,在每一种集合上建立一种数学,集合之拓广推动了数学的长足发展.建立在Extension集合之上的可拓数学既是辩证思维方法的某种创新,也是科学方法论的创新,开辟了运用数学语言、数字符号描述事物可变性的途径和方法.对正确认识客观事物可变性的哲学意蕴,以辩证的思维观、科学的哲理与方法研究它具有极其重要的意义.

Philosophic Analysis of Evolution of Set Theory

As a method used to understand objects and phenomena,set has become a key subject of modern mathematics.Set has been classified into the following three types: Cantor set,fuzzy set and extension set.The mathematical expansion for each set theory is considered as a great contribution for the development of mathematics.Extension mathematics based on extension set theory provides an approach to describe the variability of objects using mathematical languages and symbols.It gives us a new way to understand the objects and things dialectically and scientifically.There exists a great significance in studying extension mathematics in a dialectic and scientific way.